Bounds on certain classes of Kronecker and q-binomial coefficients

We present a lower bound on the Kronecker coefficients for tensor squares of the symmetric group via the characters of S-n, which we apply to obtain various explicit estimates. Notably, we extend Sylvester's unimodality of q-binomial coefficients ((n)(k)) as polynomials in q to derive sharp bounds on the differences of their consecutive coefficients. We then derive effective asymptotic lower bounds for a wider class of Kronecker coefficients. (C) 2016 Elsevier Inc. All rights reserved.